Karl Marginson's men, who'll be appearing at the penultimate qualifying stage for the first time, will start as underdogs as they lie 33 places behind the Bower Fold side.
But, having already recorded away victories over the world's oldest club, Sheffield, and UniBond premier rivals North Ferriby, the Rebels won't be overawed by a Bridge side, who hit seven in beating Stocksbridge Park Steels in the last round.
United boss Marginson said: "It's a fantastic draw for us but we know we're going to have to be at our very best to beat a team of Stalybridge's undoubted quality."
Northwich Victoria, fresh from thrashing Bardon Hill Sports 8-0, will entertain Ashton United's conquerors, Chorley, while Radcliffe or Warrington will travel to Workington.
Blyth Spartans await the winners of Hyde United's second qualifying-round tie with Salford City, which will only go ahead if the crisis-torn Tigers succeed in convincing the High Court to rescind a winding-up order served on them last week.
Should the Tigers fail and be forced into closure, Salford will go through by default.
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Free Red, Manchester (29/09/2009 at 12:53)
"Under FA Competition rules clubs with ground sharing agreements must arrange for ties to be played on Friday, Saturday or Sunday. If a clash of fixtures occurs with the sharing Club, if for any reason a tie is unable to be played on the ground of the first drawn Club on a Saturday, the tie must be played on either the day before, i.e. on Friday, or the day after, i.e. on Sunday on the ground of the First drawn Club. Therefore, our fixture will take place on Sunday 11th October 2009, kick off 3.00pm"